IQC-QuICS Math and Computer Science SeminarExport this event to calendar

Thursday, October 21, 2021 — 2:00 PM EDT

Clifford groups are not always 2-designs
Matthew Graydon, Institute for Quantum Computing

A group 2-design is a unitary 2-design arising via the image of a suitable compact group under a projective unitary representation in dimension d.  The Clifford group in dimension d is the quotient of the normalizer of the Weyl-Heisenberg group in dimension d, by its centre: namely U(1).  In this talk, we prove that the Clifford group is not a group 2-design when d is not prime. Our main proofs rely, primarily, on elementary representation theory, and so we review the essentials. We also discuss the general structure of group 2-designs. In particular, we show that the adjoint action induced by a group 2-design splits into exactly two irreducible components; moreover, a group is a group 2-design if and only if the norm of the character of its so-called U-Ubar representation is the square root of two. Finally, as a corollary, we see that the multipartite Clifford group (on some finite number of quantum systems) also often fails to be a group 2-design. This talk is based on joint work with Joshua Skanes-Norman and Joel J. Wallman; arXiv:2108.04200 [quant-ph].

Join the seminar on Zoom!
Meeting link:  https://uwaterloo.zoom.us/j/93025194699?pwd=bjVJZVpIQXJkS1U2aXg2d3Q3QVhBdz09

Add event to calendar

Apple   Google   Office 365   Outlook   Outlook.com   Yahoo

This virtual seminar is jointly sponsored by the Institute for Quantum Computing and the Joint Center for Quantum Information and Computer Science.


If you are interested in presenting at a future seminar, please email either Daniel Grier (daniel.grier@uwaterloo.ca) or Hakop Pashayan (hpashaya@uwaterloo.ca).

S M T W T F S
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
2
3
4
5
6
  1. 2021 (45)
    1. November (2)
    2. October (5)
    3. September (3)
    4. August (4)
    5. July (4)
    6. June (5)
    7. May (3)
    8. April (4)
    9. March (5)
    10. February (4)
    11. January (6)
  2. 2020 (31)
    1. December (2)
    2. November (5)
    3. October (4)
    4. September (3)
    5. August (2)
    6. June (4)
    7. April (1)
    8. March (3)
    9. February (5)
    10. January (2)
  3. 2019 (139)
  4. 2018 (142)
  5. 2017 (131)
  6. 2016 (88)
  7. 2015 (82)
  8. 2014 (94)
  9. 2013 (91)
  10. 2012 (122)
  11. 2011 (117)
  12. 2010 (41)
  13. 2009 (4)
  14. 2008 (1)
  15. 2005 (1)
  16. 2004 (3)